1. Technical Field
This invention relates generally to projectiles and more specifically to a projectile and a method of launching a projectile from a barrel to produce a controlled spin rate.
2. Background Art
Where the gyroscopic stability factor, Sg, of a projectile in flight exceeds one, a gyroscopic stability condition is present. The gyroscopic stability factor may be defined as follows:
Sg=(Ix/Iy)xc3x97(pd/Vw)xc3x97(2Ix/xcfx81xcfx80d5) 
where:
Ix=axial moment of inertia of the projectile
Iy=forward moment of inertia of the projectile
Vw=velocity
d=projectile diameter
p=spin rate of the projectile
xcfx81=air density
Alternately, the gyroscopic stability factor may be defined as follows:
Sg=P2/4M=Ix2p2/2pIySdV2CMxcex1
where,
P=the sum of epicyclic turning rates
M=mach number
Ix=axial moment of inertia of the projectile
p=projectile axial spin in radians/second
Iy=forward moment of inertia of the projectile
S=projectile reference area S=d2/4
d=projectile diameter
V=velocity
CMxcex1=pitching moment coefficient
The relationship between the axial moment of inertia Ix and the forward moment of inertia of the projectile Iy is readily observed. Additionally the above expressions attempt to characterize the relationship between a projectile""s forward velocity, spin rate and geometry and the effect that these variables may have on gyroscopic stability.
It is generally believed that a projectile may be made gyroscopically stable by increasing the spin rate of the projectile. It is also widely believed that if a projectile is gyroscopically stable at the muzzle, it will be gyroscopically stable throughout its flight.
Practically speaking, however, the spin rate p decreases more slowly than the forward velocity, and therefore, the gyroscopic stability factor Sg, continues to increase throughout the flight of the projectile. Designers usually prefer a gyroscopic stability factor Sg greater than 1.2 to 1.5 at departure from the muzzle, but because spin rate decreases more slowly than the forward velocity it is also possible to introduce too much spin to a projectile. This condition is commonly characterized as xe2x80x9cover-stabilizationxe2x80x9d. It has been observed that a projectile may become unstable by being xe2x80x9cover-stabilizedxe2x80x9d, however, most designers and commentators have not been terribly concerned with this aspect of flight as it is also commonly held that small arm fire is ineffective past the range where instability due to xe2x80x9cover-stabilizationxe2x80x9d may occur, for instance, in the range of 2000 to 4000 yards.
xe2x80x9cOver-stabilizationxe2x80x9d is a popular mischaracterization used to describe a phenomenon wherein the axial speed of the projectile continues to increase in proportion to the forward speed. As a result, the projectile becomes incapable of following the bending trajectory and the longitudinal axis of the projectile continues to nose up in relation to the bending trajectory. This effect may be referred to as a decrease in tractability. The relationship between excess gyroscopic stability and lack of stability in flight has been previously observed. FIG. 11 is a schematic representation depicting the relationship between gyroscopic stability GS and distance D in two projectiles manufactured and launched according to the prior art, a 7.62 mm and a 50 caliber. As can be readily seen, in each case the value for gyroscopic stability GS effectively continues to increase from the muzzle until termination of flight at T in the range of 2300 to 2500 yards. As will be seen, the relationship between a maximum GS value and a starting GS value produces the following ratios: 7.62 mmxe2x80x94approximately 9.50:2.20 or 4.32:1 and 50 caliberxe2x80x94approximately 5.60:1.60 or 3.50:1.
Skin friction at the surface of the projectile has a direct effect on the axial velocity of a projectile. A spin damping coefficient MS may be defined as follows:
MS=xe2x88x92(xcfx81/2)xc3x97Axc3x97Cspin(Bxc3x97Maxc3x97Re)xc3x97Vw2xc3x97d(pd/Vw)xc3x97ec 
where:
xcfx81=air density
A=projectile cross section area
Cspin=the spin damping moment coefficient
B=projectile geometry
Ma=mach number
Re=Reynolds number
VW=velocity
d=projectile diameter
p=spin rate of the projectile
ec=unit vector in the direction of the projectile""s longitudinal axis
A spin damping moment may be defined as follows:
xc2xdxcfx81V2Sd(pd/V)Cspin 
where:
xcfx81=air density
V=projectile velocity
S=projectile reference area
d=projectile diameter
p=spin rate of the projectile
Cspin=the spin damping moment coefficient
The relationship between the spin damping moment coefficient and the spin damping moment may be observed in the above formulas. Particularly, the greater the spin damping moment coefficient for any given atmospheric condition, projectile geometry, projectile velocity, both axial and forward and the ratio of axial spin to forward velocity, the greater the spin damping moment. The relationship between spin damping moment coefficient and forward velocity has likewise been observed.
FIGS. 12A and 12B are schematic representations depicting generally the relationship between axial deceleration, forward deceleration and distance in two projectiles of the prior art, a 7.62 mm and a 50 caliber. As can be seen in either case, the rate of decrease in forward deceleration exceeds the rate of decrease in axial deceleration in both cases and as a result, there is an increased probability of the occurrence of xe2x80x9cover-stabilizationxe2x80x9d and as a result, instability in flight.
FIG. 13 is a schematic representation depicting the relationship between spin damping moment coefficient, SDMC, and forward velocity, MACH, in two projectiles manufactured and launched according to the prior art, a 7.62 mm and a 50 caliber. As can be seen, in each case the spin damping moment coefficient in either case remains in the range of approximately xe2x88x920.018 to xe2x88x920.027 regardless of forward velocity.
The relationship characterized by the expression pd/V, projectile diameter times the spin rate of the projectile divided by the velocity, expressed in spin per caliber of travel, has also been previously observed. FIG. 14 is a schematic representation depicting the relationship between projectile diameter times the spin rate of the projectile divided by the velocity, pd/V, and distance D in two projectiles manufactured and launched according to the prior art, a 7.62 mm and a 50 caliber. As can be readily seen, in each case the spin per caliber of travel effectively continues to increase from the muzzle until termination of flight at T in the range of 1300 to 2500 yards. Additionally, the relationship between a maximum pd/V value and a starting pd/V value produces the following ratios: 7.62 mmxe2x80x94approximately 4.22:1.94 or 2.17 and 50 caliberxe2x80x94approximately 5.07:2.35 or 2.15. In each instance, it should be noted that the value for pd/V, at termination of flight, may be characterized as increasing.
It may be advantageous to the efficiency of a projectile""s flight to control the spin damping moment coefficient of the projectile by controlling various parameters of projectile design including projectile aerodynamics, projectile surface area and projectile surface features and finish. By controlling the spin damping moment coefficient the gyroscopic stability factor may be maintained within a predetermined desirable range and overall ballistic efficiency maybe improved.
The present invention is directed to a projectile and a method of launching a projectile from a barrel, the projectile having an axial velocity upon launching. The projectile of the present invention may be matched to a pre-selected barrel rifling to produce a controlled spin rate. xe2x80x9cControlled spin ratexe2x80x9d, as used herein, is characterized by substantially balanced forward and axial deceleration. xe2x80x9cSubstantially balanced forward and axial decelerationxe2x80x9d, as used herein, is characterized by an axial speed that decreases in relationship to the decrease in forward speed. Substantially balanced forward and axial deceleration produces a trajectory that may be depicted by a curve exhibiting a relatively narrow band of values for the gyroscopic stability factor over a given distance of a trajectory.
Gyroscopic stability is controlled during the projectile""s flight by controlling the spin damping moment as a design element. More particularly, control of the spin damping moment may result from a projectile design that incorporates a relatively low aerodynamic drag value with physical features incorporated in the projectile""s design and manufacture, or produced during launch, that increase the skin friction at the surface of the projectile. Alternately, the projectile may include both physical features incorporated in the projectile""s during manufacture and physical features which are imparted upon the projectile during launch.
In one preferred embodiment of the invention, a projectile is provided having a relatively low density and a relatively low drag coefficient. A projectile manufactured and launched according to the present invention exhibits a drag coefficient in the range of 0.100 to 0.250. A physical feature is then identified and selected that will produce a pre-selected projectile surface area and/or surface relief that produces a calculated spin damping moment. For instance a projectile may be matched to a barrel including riflings that produce physical scoring on the exterior surface of the projectile which cover a predetermined percentage of the exterior surface of the projectile to produced a controlled effect on the spin damping moment resulting in a controlled deceleration of axial velocity of the projectile during flight.
In one preferred embodiment of the invention, the spin stabilized projectile is manufactured having sufficiently low aerodynamic drag so that upon launching, the ensuing axial drag, as increased by designed physical features, will cause the projectile to exhibit a controlled spin rate and controlled axial deceleration. The trajectory of such a projectile is characterized by substantially balanced forward and axial deceleration. The result is a projectile which is aerodynamically stable while not being overspun to the point of induced instability. The lower aerodynamic drag and the increased axial drag are substantially balanced throughout the projectile""s flight to produce a controlled spin and increase in the spin damping moment. During flight, the gyroscopic stability of the projectile is not increasing or decreasing dramatically.
The gyroscopic stability factor of a projectile of the present invention, a projectile exhibiting substantially balanced forward and axial deceleration, should remain in the range of greater than or equal to 1.0 to less than or equal 3.0. Alternately, the gyroscopic stability factor of a projectile of the present invention, a projectile exhibiting substantially balanced forward and axial deceleration, should remain in the range of greater than or equal to 1.0 through and including three times the initial value at the muzzle. A projectile manufactured and launched according to the present invention, should exhibit increased tractability and stability particularly down range. Balancing forward and axial deceleration should produce a trajectory that is characterized by a nose that maintains a near direct into oncoming air orientation throughout its trajectory. The gyroscopic stability factor of the projectile increases or decreases only within a relatively narrow range.
Physical features which may contribute to a calculated control of a projectile""s spin damping moment include but are not limited to the total surface area of the projectile, the length of the projectile, the length, depth and number of lands and grooves engraved by barrel riflings on launch, surface roughness and material density of the projectile. Controlled axial drag imparts a controlled axial deceleration. Physical features which may be calculated to affect the spin damping moment include but are not limited to the following:
a. control of projectile total surface area and total axial surface friction;
b. decrease in the density of constituent materials;
c. control of the number of lands and grooves in the rifle bore from which the projectile is shot and engraved, thereby controlling the number of engraved grooves on the projectile;
d. control of the length of engraving to control axial deceleration;
e. control of the depth of engraving to control axial deceleration;
f. control of the forms of engraving using trigonal, polygonal, and multi-cornered shapes to increase axial drag to control axial deceleration;
g. incorporation of fins, canards, wings, deflectors, and protrusions to control axial deceleration;
h. control of the surface roughness of the projectile to control axial deceleration;
i. any other feature manufactured into the projectile or caused by the engraving process which by effect controls the spin dampening moment and causes a gyroscopic balance the projectile""s trajectory.
It is believed that the control of spin damping moment by the control and specification of physical features provides a projectile which in flight maintains gyroscopic stability within a specified range preventing increased yaw, increased precession, increased inaccuracy and projectile instability.
Historically, designers of projectiles for small arms have not been concerned with ballistic efficiency or the effects of xe2x80x9cover-stabilizationxe2x80x9d, primarily instability, at ranges beyond 2000 yards as it is commonly held that small arm fire is ineffective past this range. A projectile engraved and launched according to the teachings of the present invention, however, is designed to decelerate from supersonic flight through transonic to subsonic in a stable and predictable manner effective in a range beyond 3000 yards.
The present invention consists of the combination and arrangement of parts hereinafter more fully described, illustrated in the accompanying drawings and more particularly pointed out in the appended claims, it being understood that changes may be made in the form, size, proportions and minor details of construction without departing from the spirit or sacrificing any of the advantages of the invention.